You are quite wrong.
According to my experience and to the stats stormpios and assault engis are fairly equal dps wise on their effective ranges, usually positioning, closing in decides who wins this engagement.
Ingame the Stg44 of Stormpios behave more like SMGs statewise, since their Stg44 differs from the Panzergrenadier ones.
Historically, the Stg44 had also a higher rate of fire if compared to the Grease gun.
Now check the Assault Grenadiers , they have less dps, while costing the same and having less utility(but at least they have one additional entity )
This shows that Assault Engis are perfectly fine.
Sturmpios 57 range 1 dps assengies 48 range 1 dps. That is not equal.
In my experience assengies never win point blank, even coming around a wall at point blank range they didn't even kill a sturmpio before being wiped. Although personal experience means nothing on this forum so whatever.
A higher rate of fire on an assault rifle means nothing when you can't control it compared to a 9mm submachine gun. When I was in the US Marines I learned to fire my M249 SAW at point blank range, that thing has a sweet rate of fire, but I would rather have a submachine gun in close quarters.